How Can I Infer the Expression of A in a Non-Trivial Solution?

  • Thread starter Ribena
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In summary: Exactly, so I was wondering if there was any way in general to infer the expression of x. I think the only way is to perhaps add a constraint that does not result in an infinite solution case, but if possible, I didn't want to change the original constraints.There is no way to know the expression for x without knowing g and h, but there are methods you could try that would not require changing the original constraints. There is no way to know the expression for x without knowing g and h, but there are methods you could try that would not require changing the original constraints.
  • #1
Ribena
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Hi all,

So I've been trying to solve a system of 'linear' equations and I understand that for a non trivial solution to exist you have to get the determinant to reduce to zero.

Given that you have an equation which takes the form

(f(x))*A=0, where f(x) is an arbitary function and A is a constant, the solution is either f(x)=0 or A=0.

Now say that for a non trivial solution, I'd require that f(x)=0, is there any methods in general in which I can obtain an expression for A? Let's assume it's a 4 by 4 system of equation.
 
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  • #2
What are f(x) and A? Matrices?
 
  • #3
Erland said:
What are f(x) and A? Matrices?

Polynomials.
 
  • #4
Ribena said:
Polynomials.
How can it then be a 4x4 system of equations?

No, you must more clearly specify what you mean...
 
  • #5
Erland said:
How can it then be a 4x4 system of equations?

No, you must more clearly specify what you mean...

Ah, I get what you mean now. I'm not from a mathematical background so do bear with me is some of my definitions are not precise. So I basically have 4 equations with 4 unknowns to solve let's assume that they are w,x,y,z. By eliminating the variables, I've managed to bring them down a single equation that looks something like (2g+h)*(x)=0 where g and h are predefined constants.

So for a non trivial solution to exist, then (2g+h)=0. Will it be possible then to know the expression for x in terms of g and h (if one exists at all)?

Hopefully it's not too confusing
 
  • #6
Ribena said:
So for a non trivial solution to exist, then (2g+h)=0. Will it be possible then to know the expression for x in terms of g and h (if one exists at all)?
But if 2g+h=0, then any value of x will do.
 
  • #7
Erland said:
But if 2g+h=0, then any value of x will do.

Exactly, so I was wondering if there was any way in general to infer the expression of x. I think the only way is to perhaps add a constraint that does not result in an infinite solution case, but if possible, I didn't want to change the original constraints.

Just wanted to seek some opinions to see if there actually is some method that I was unaware of.
 

FAQ: How Can I Infer the Expression of A in a Non-Trivial Solution?

How do you approach finding a solution to (A)(B)=0?

The first step in finding a solution to (A)(B)=0 is to understand the problem at hand. This includes identifying the variables A and B and any other relevant information. Next, you will need to manipulate the equation to isolate either A or B on one side of the equation. Finally, you can solve for the remaining variable using basic algebraic principles.

What if there are multiple solutions to (A)(B)=0?

If there are multiple solutions to (A)(B)=0, it means that there are multiple combinations of A and B that will result in the product equaling zero. In this case, you can list out all possible solutions or use a graphing calculator to visualize and identify the solutions.

Can (A)(B)=0 have no solutions?

Yes, it is possible for (A)(B)=0 to have no solutions. This would occur if the values of A and B cannot be manipulated to result in a product of zero. In other words, there is no combination of A and B that would make the equation true.

Are there any special cases to consider when finding a solution to (A)(B)=0?

Yes, there are a few special cases to consider when finding a solution to (A)(B)=0. One is when one of the variables, A or B, is equal to zero. In this case, the other variable can be any value, and the product will still equal zero. Another special case is when both A and B are equal to zero, resulting in a product of zero as well.

How can finding a solution to (A)(B)=0 be applied in real-life situations?

Finding a solution to (A)(B)=0 can be applied in various real-life situations, such as calculating break-even points in business, determining the roots of a quadratic equation in mathematics, or solving for unknowns in physics equations. It is a fundamental problem-solving skill that can be used in many different fields of study.

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